Version 1
: Received: 23 August 2024 / Approved: 26 August 2024 / Online: 27 August 2024 (10:58:58 CEST)
How to cite:
Pelissier, U.; Parret-Freaud, A.; Bordeu, F.; Mesri, Y. Graph Neural Networks for Mesh Generation and Adaptation in Structural and Fluid Mechanics. Preprints2024, 2024081947. https://doi.org/10.20944/preprints202408.1947.v1
Pelissier, U.; Parret-Freaud, A.; Bordeu, F.; Mesri, Y. Graph Neural Networks for Mesh Generation and Adaptation in Structural and Fluid Mechanics. Preprints 2024, 2024081947. https://doi.org/10.20944/preprints202408.1947.v1
Pelissier, U.; Parret-Freaud, A.; Bordeu, F.; Mesri, Y. Graph Neural Networks for Mesh Generation and Adaptation in Structural and Fluid Mechanics. Preprints2024, 2024081947. https://doi.org/10.20944/preprints202408.1947.v1
APA Style
Pelissier, U., Parret-Freaud, A., Bordeu, F., & Mesri, Y. (2024). Graph Neural Networks for Mesh Generation and Adaptation in Structural and Fluid Mechanics. Preprints. https://doi.org/10.20944/preprints202408.1947.v1
Chicago/Turabian Style
Pelissier, U., Felipe Bordeu and Youssef Mesri. 2024 "Graph Neural Networks for Mesh Generation and Adaptation in Structural and Fluid Mechanics" Preprints. https://doi.org/10.20944/preprints202408.1947.v1
Abstract
Finite element discretizations of problems in computational physics often rely on hand-generated initial mesh and adaptive mesh refinement (AMR) to preferentially resolve regions containing important features during simulation. We propose Adaptnet, a Graph Neural Networks (GNNs) framework for learning mesh generation and adaptation. The model is composed of two GNNs: the first one, Meshnet, learns mesh parameters commonly used in open-source mesh generators, to generate an initial mesh from a Computer Aid Design (CAD) file; while the second one, Graphnet, learns mesh-based simulations to predict the components of an Hessian-based metric to perform anisotropic mesh adaptation. Our approach is tested on structural (Deforming plate - Linear elasticity) and fluid mechanics (Flow around cylinders - steady-state Stokes) problems. Our results show it can accurately predict the dynamics of the system and adapt the mesh accordingly. The adaptivity of the model supports learning resolution-independent dynamics and can scale to more complex state spaces at test time.
Computer Science and Mathematics, Computational Mathematics
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
